Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1187
... operator the resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For in p ( T ) the symbol R ( 2 ; T ) will be used for the ...
... operator the resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For in p ( T ) the symbol R ( 2 ; T ) will be used for the ...
Page 1290
... operator of order n . Indeed , let ▾ be such an operator , and let its leading coefficient be a ,. Then the leading coefficient in t * is ( -1 ) " a ; thus , if n is even , a , is real , while if n is odd , a , is pure imaginary . If n ...
... operator of order n . Indeed , let ▾ be such an operator , and let its leading coefficient be a ,. Then the leading coefficient in t * is ( -1 ) " a ; thus , if n is even , a , is real , while if n is odd , a , is pure imaginary . If n ...
Page 1540
... operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal differential operator on ...
... operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal differential operator on ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero